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KCET2020MathematicsTrigonometric Ratios & Identities

Events E₁ and E₂ from a partition of the sample space S . A is any event such that P (E₁ )=P (E₂ )= 1 2 , P (E₂ / A )= 1 2 and P (A / E₂ )= 2 3 , then P (E₁ / A ) is

Options

  1. A1 2
  2. B2 3
  3. C1
  4. D1 4

Correct answer

A. 1 2

Step-by-step solution

Given P (E₁ )=P (E₂ )= 1 2 aligned P (E₂ / A ) &= 1 2 , P (A / E₂ )= 2 3 P (E₁ / A ) &= P (E₁ ) P (A / E₁ ) P(A) P (E₂ / A ) &= P (E₂ ) P (A / E₂ ) P(A) P (E₁ / A ) &+P (E₂ / A )=1 P (E₁ / A ) &=1-P (E₂ / A ) &=1- 1 2 = 1 2 aligned

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